Mail Service

For all intents and purposes, there is no functional mail service on the island.  Technically, there is, but it takes months for things to be delivered to the post office, and you may have to go check and sort through it all yourself.

If you're looking to get mail forwarded from the US to here, there are courier services for that.  It depends on where your mail is coming from and going to.  Most people get their mail delivered to a family member or friend that you trust, and they can filter and send pictures of the important pieces. 

For packages, find a courier close to where you live in the DR (Mailboxes, Domex, EPS or whatever) and open an account with them.  They give you an address in Miami for Amazon or whoever to deliver to, and they transport the package to the DR.  They range in price from $4 or $5 a pound, and some offer delivery to you home.  You need to register your passport with Customs here as well.

Alternatively, Amazon offers some products directly shipped to the DR.  It takes a little longer, some items are more expensive, and not all items are available for this, you need to select your DR address before you begin shopping on Amazon.

Not too difficult, but it is different.

@Scott Holmes

The Dominican Republic technically has a public postal service called INPOSDOM, but standard home mail delivery like you have with the USPS doesn't really exist for everyday residential addresses. There are rarely street-side mailboxes, addresses can be incredibly confusing, and the public system is notoriously slow and unreliable for international mail.